Let Y be an exponential random variable, where f Y (y) = e y, 0 y. For any positive integer n, show that

Let Y be an exponential random variable, where f_Y(y) = λe^−λy, 0 ≤ y. For any positive integer n, show that P(n ≤ Y ≤ n + 1) = e^−λn(1 − e^−λ). If p = 1 − e^−λ, the "discrete" version of the exponential pdf is the geometric pdf.